Well, your game is saved automatically. It just might be, that you can't see it any more because your IP (or whatever) changed. I don't know what criteria Farin used to let you access your saved games again, but it is not the user name, as yesterday I could enter a game with the user name "test" that I started as "Safari". I guess it is something that depends on your device.
However, online games are saved up to 7 days (not sure about the days, but I think Farin mentioned 7).